Four-wave mixing with matter waves

Abstract

letters to nature 218 NATURE | VOL 398 | 18 MARCH 1999 | www.nature.com optimizing the performance of the interferometers at low frequencies, where both equations (4) and (6) become more signi®cant. It appears natural to perform such studies in the quiet environment of space, perhaps through future re®nements of LISA-type set-ups 27 .The above discussion of gravity-wave interferometers shows that the smallness of the Planck length does not preclude the possibility of direct investigations of space-time fuzziness. This complements the results of studies 28,29 which have shown that indirect evidence of quantum space-time¯uctuations could be obtained by testing the predictions of theories consistent with a given picture of thesē uctuations. Additional encouragement for experiment-driven progress in understanding the interplay between gravity and quantum mechanics comes from recent studies 30,31 in the area of gravitationally induced phases, the signi®cance of which has been emphasized in refs 32 and 33. M

Statics and dynamics of a self-bound dipolar matter-wave droplet

“…The higher order nonlinearity (quintic) of the three-body interaction compared to the cubic nonlinearity of the two-body interaction, has led to a more singular repulsive term at the origin in (6). This makes the system highly repulsive at the center (w ρ , w z → 0), even for a small three-body repulsion, and stops the collapse stabilizing the droplet.…”

“…The stationary widths w ρ and w z of a droplet correspond to the global minimum of energy (6) [26,27] 1 (8) and (9), for different K 3 . For N < N crit and for a > a dd = 15.3a 0 (dipolar) and for a > 0 (nondipolar) no droplet can be formed.…”

Spinor Condensates and Light Scattering from Bose-Einstein Condensates

“…14B). Those higher-order peaks may also be affected by stimulated Raman scattering and four-wave mixing between matter waves [39] which couple the different recoil modes. The angular pattern of the emitted light along the axial direction showed a few bright spots with an angular width θD (1/e 2 diameter) of 107 ± 20 mrad, corresponding to the diffraction limited angle of an object of ∼ 14 µm in diameter.…”

“…The strength of the confining field could be easily modified by adjusting the currents through the magnetic trapping coils, allowing us to vary the peak condensate density in the range (0.5 -6) ×10 14 cm −3 and the radial half-width of the condensate (x c ) between 7 and 15 µm. The two laser beams used for Bragg scattering were derived from a common source, and had a detuning to the red of the 3S 1/2 , |F = 1 → 3P 3/2 , |F ′ = 0, 1, 2 optical transitions of about ∆ = 1.7 GHz (similar parameters were used for experiments at NIST, Gaithersburg [14,15,38,39]). A small frequency difference ω between the counter-propagating beams, on the order of 2π × 100 kHz, was introduced by using two independently-controlled acousto-optic modulators (AOM's) to control the frequency of two independent beams 2 .…”

RF-Induced Evaporative Cooling And BEC In A High Magnetic Field

“…Bose-Einstein condensates [1][2][3] are very promising for atom optics [4][5][6] , where they are expected to play a role as important as lasers in photon optics, since they are coherent sources of atoms with a very large luminosity. In view of applications, it is crucial to develop apparatuses that produce BEC fasterthe average production rate of a condensate is 0.01 Hz -and with more versatile designs, by reducing, for example, the power consumption of the electromagnets.…”